J. Membrane Biol. 106, 123-134 (1988)

Tho Journal of

MembraneBiology 9 Springer-Verlag New York Inc. 1988

Electrophysiological Properties of Dictyostelium Derived from Membrane Potential Measurements with Microelectrodes Bert Van D u i j n , t $ Dirk L. Ypey,:~ and L o e k G. Van der M o l e n ? tCell Biology and Genetics Unit, Zoological Laboratory, University of Leiden, NL-2300 RA Leiden, The Netherlands, and +Department of Physiology and Physiological Physics, University of Leiden, NL-2333 AL Leiden, The Netherlands

Summary. Electrical membrane properties of the cellular slime mold Dictyostelium discoideurn were investigated with the use of intracellular microelectrodes. The rapid potential transients (1 msec) upon microelectrode penetration of normal cells had a negative-going peak-shaped time course. This indicates that penetration of a cell with a microelectrode causes a rapid depolarization, which can just be recorded by the microelectrode itself. Therefore, the initial (negative) peak potential transient value Ep ( - 19 mV) should be used as an indicator of the resting membrane potential Em ofD. discoideum before impalement, rather than the subsequent semistationary depolarized value En (-5 mV). Using enlarged cells such as giant mutant cells (Ep = 39 mV) and electrofused normal cells (Ep = -30 mV) improved the reliability of Ep as an indicator of Era. From the data we concluded that Em of D. discoideum ceils bathed in (raM) 40 NaCI, 5 KC] and 1 CaCI2 is at least -50 inV. This potential was shown to be dependent on extracellular potassium. The average input resistance Ri of the impaled cells was 56 Mf~ for normal D. discoideum. However, our analysis indicates that the membrane resistance of these cells before impalement is >1 GO. Specific membrane capacitance was 1-3 pF/cm 2. Long-term recording of the membrane potential showed the existence of a transient hyperpolarization following the rapid impalement transient. This hyperpolarization was associated with an increase in R~ of the impaled cell. It was followed by a depolarization, which was associated with a decrease in Ri. The depolarization time was dependent on the filling of the microelectrode. The present characterization of the electrical membrane properties of Dictyostelium cells is a first step in a membrane electrophysiological analysis of signal transduction in cellular slime molds. Key Words membrane potential. Dictyostelium discoideum 9 microelectrode 9 peak transient - hyperpolarization 9 potassium conductance Introduction T h e cellular slime m o l d Dictyostelium discoideurn p r o v i d e s a g o o d m o d e l s y s t e m for studying transm e m b r a n e signal t r a n s d u c t i o n and the role o f signal t r a n s d u c t i o n in cellular differentiation. This simple o r g a n i s m has a t w o - s t a g e life cycle, consisting o f a unicellular vegetative stage and a multicellular ag-

gregated stage, in the vegetative stage, D. discoideum is a free, in the soil, living a m o e b a feeding on bacteria. T h e multicellular stage develops by aggregation o f the cells i n d u c e d by e x h a u s t i o n o f the f o o d supply. A g g r e g a t i o n is m e d i a t e d by a c h e m o a t tractant, w h i c h is s e c r e t e d by the cells and has been identified as cyclic A M P (cAMP) [17]. The multicellular aggregates f o r m fruiting bodies producing spores. During aggregation, c A M P acts as an extracelM a r h o r m o n e - l i k e signaling agent and is d e t e c t e d by cell surface receptors. Binding o f c A M P to the c A M P r e c e p t o r s induces a variety o f intracellular r e s p o n s e s , including a rapid but transient activation o f a d e n y l a t e c y c l a s e and g u a n y l a t e c y c l a s e [8, 27]. Various e x p e r i m e n t s indicate a possible role for ions in the c A M P signal transduction. F o r example, the addition o f c A M P to suspensions o f D. discoideum results in c h a n g e s in extracellular calcium[5, 6, 20] and p o t a s s i u m - c o n c e n t r a t i o n s [1]. Potassium and calcium fluxes m a y reflect c h a n g e s in m e m b r a n e c o n d u c t a n c e and potential. Therefore, k n o w l e d g e o f the m e m b r a n e potential o f D. discoideum and its ionic m e c h a n i s m is required to study the role of t r a n s m e m b r a n e ionic currents in t r a n s m e m b r a n e signal transduction. F u r t h e r m o r e , the interpretation o f single ion channel m e a s u r e m e n t s in these cells also requires k n o w l e d g e of the m e m b r a n e potential [22]. G i v e n the e x t e n s i v e k n o w l e d g e o f biochemical m e c h a n i s m s o f signal t r a n s d u c t i o n in D. discoideum d e v e l o p e d in the last years [8, 27], the application o f m e m b r a n e e l e c t r o p h y s i o l o g i c a l techniques m a y p r o v i d e n e w insights into the m e c h a n i s m o f signal t r a n s d u c t i o n in D. discoideum. T h e availability o f D. discoideum m u t a n t s with k n o w n defects in signal t r a n s d u c t i o n m a y then be o f great use in this approach. Dictyostelium cells can survive in rapidly c h a n g i n g ionic conditions, w h i c h indicates a p o w e r -

124

ful regulation of intracellular ion concentrations [21]. This regulation, probably by a combined action of ion pumps and ion channels, may also be expected to involve membrane potential control. The patch-clamp technique in the whole-cell configuration cannot always be used to determine membrane potentials and membrane potential changes. On many cell types giga-seal formation is not yet possible. So far, no giga-seals on Dictyostelium cells bathed in normal saline solutions (i.e., solutions containing potassium and <1 mM Ca 2+) could be made [22; unpublished observations]. Enzyme treatment to facilitate giga-seal formation may damage the membrane. The exchange of the normal intracellular constituents of the cell and the clamping of artificial intracellular ion concentrations (especially calcium) in the whole-cell configuration are draw backs in the use of the patch-clamp technique in the study of the effect of drugs on the membrane potential. Microelectrode measurements, when applied carefully, provide a method to directly measure the membrane potential of intact cells. Since microelectrode penetration induces a transmembrane shunt resistance, microelectrode measurements, especially in small cells, should be interpreted with care [13, 18]. This shunt resistance is probably located in the hydration mantle surrounding the microelectrode. Membrane potential measurements with microelectrodes in high-resistance cells usually suffer from sustained depolarization of the resting membrane potential due to the transmembrane shunt resistance [2, 13, 16, 24]. However, an analysis of the fast potential transient occurring within the first milliseconds after impalement may still provide information about the preimpalement electrical membrane properties of the cell [13]. Because Dictyostelium cells are relatively small (diameter < 10/xm), a sustained depolarization of the membrane potential upon microelectrode impalement might be present. In the present study, we report membrane potential measurements in Dictyostelium including an analysis of the fast potential transient upon microelectrode impalement. Enlargement of cells is introduced as a method to check the reliability of the peak potential transient as a measure of the true membrane potential. We evaluate the application of microelectrodes in these cells and give an estimation of the membrane potential, resistance and capacitance of D. discoideum cells bathed in a Na § saline solution. Our results are evidence that the potassium equilibrium potential as well as electrogenic ion pumps contribute to the membrane potential of D. discoideum. The present study provides an electrophysiological basis for future research involving the role of

B. Van Duijn et al.: Membrane Potential of Dico'osteli,m

ions and ion channels in transmembrane signal transduction of D. discoideum. Materials and Methods CELL CULTURE CONDITIONS Cells used for experiments included three types ofD. discoideum cells. First, D. discoideum NC4-H, which was grown together with Escherichia coli 281 on solid medium containing 3.3 g peptone, 3.3 g glucose, 4.5 g KH_~PO4, 1.5 g Na_,HPO4 - 2H20, and 15 g agar per liter. After 40 hr incubation at 22~ the cultures were harvested with cold 10 mM sodium/potassium phosphate buffer (pH 6.5). The cells were washed free of bacteria by three washes and by centrifugation at 150 x g for 2 min. Subsequently, the cells were deposited on glass cover slips, with thickness of 0.17 mm (roughly 5 • l04 cells/cm-'), in petri dishes and stored for at least 2 hr, but not longer than 4 hr, at room temperature. Second, electrofused D. discoideum cells were used [23]. After harvesting and washing, the cells were resuspended in 10 mM sodium/potassium phosphate buffer (10~ cells/ml). Cell fusion was accomplished by four pulses of 5 kV/cm with 3-sec interval. Thereafter, the cell suspension was handled in the same way as the normal cells. The cell suspensions treated in this way contained, in addition to cells of normal size, some cells of remarkably increased size. The large cells from these suspensions were used for experiments. Additionally, we used mutant Dictyostelium cells with disrupted myosine heavy-chain gene, called hmm-cells [7]. These cells exhibit relatively normal karyokinesis but limited cytokinesis, causing the formation of large cells. The cAMP-induced cAMP, cGMP and chemotactic responses in hmm-cells were not altered as compared with normal cells [26]. The hmm-cells were grown on plastic support in HL5-medium supplemented with 20 U/ml streptomycin/penicillin and 10/xg/ml G418 (Sigma Chemical Co.). The cells were harvested with growth medium and collected by centrifugation at 150 x g for 2 min. Subsequently, the cells were resuspended in 10 mM sodium/potassium buffer and deposited on glass cover slips. The membrane area of all the cells used was estimated by taking two times the area enclosed by the estimated cell circumference. Since these cells are rather flat, this appeared to be the best method to estimate the membrane area of cells adhered to the glass cover slip. During experiments, the cells were bathed in a Na+-saline solution composed 0f40 mM NaC1, 5 mM KC1, 1 m g CaC12 and 1 mM HEPES-NaOH (pH 7.0). D. discoideum cells showed normal development when starved on solid medium containing Na*saline solution and 15 g agar per liter. The K+-saline solution used consisted of 50 mM KC1, 5 mM NaC1, 1 mM CaCI2 and 1 mM HEPES-KOH (pH 7.0). Furthermore, a Ca2--saline solution was used composed of 10 mM Ca(Cyclamateh, 10 mM CaCI~ and 1 mM HEPES-KOH (pH 7.2).

ELECTROPHYSIOLOGY For electrophysiological experiments, the glass cover slips with the adhered cells were mounted to an open-bottom Teflon culture dish, which placed on the stage of an inverted microscope permitted measurements using an objective magnification of 100• with oil immersion optics [14]. Membrane potential measurements were made with microelectrodes and a microelectrode amplifier with capacitance corn-

B. Van Duijn et al.: Membrane Potential of Dictyostelium

125

Table. Membrane electrophysio}ogica] properties (mean vatues) of normal D. discoidemn cells {DdH), electrofused D. discoideum cells (DdHfused) and giant mutant cells (hmm), bathed in Na--saline solution ~'

DdH (SD,n) DdHfused (SD,n) hmm (SD,n)

El, (mY)

E,, (mV)

t,, (msec)

A re a (/~m -~)

Ri

C,,,

El,

TI/~_

(M[~)

(pF)

(mV)

(sec)

- 19.1 (3.8, 32) -30.2 (5.0, 36) -38.9 (4.2, 127)

-4.7 (1.6, 32) 6.0 (2.0, 36) - 12.0 (2.0, 127)

0.09 (0.02, 32) 0.13 (0.05, 36) 0.54 (0.22, 127)

88 (52, 32) 790 (410, 36) 1724 (181, 127)

56 (14, 10) 33 ( l l , 26) 35 (12, 29)

6.1 (0.8, 10) --

- 12.1 (4.6, 24) - 10.7 (4.7, 15) - 15.8 (6.1, 45)

1.9 (1.4, 24) 3. l (2.5, 15) 6.5 (4.9, 45)

[ 2.2 (3.9, 29)

Given are: Ep, the peak value of the fast potential transient observed upon impalement as indicated in the text. E,,, the depolarized " s t e a d y - s t a t e " potential, which is reached just after Ep has appeared, t,,, the time to reach two-thirds of the depolarization to E,, after Ep was reached. Area, the estimated membrane area measured as indicated in the text. R~, input resistance of the impaled cells just after the potential reached the value E,,. C,,,, capacitance of the cell membrane determined as indicated in the text. Eh. the maximal hyperpolarized potential after E,, was reached. /~:, the time to reach one-half of the depolarized potential after E~, was reached. All differences measured between the three cell types of the different electrophysiological properties are significant (Student's t test, 97.5% level) except for R~ of DdHfused and hmm cells, and Eh and Ti.,_,of DdH and DdHfused cells.

pensation (WP1 Series 700 Micro Probe Model 750, WP Instruments, New Haven, CT). Fine-tipped open-end microelectrodes with wide-angle tapers, filled with 3 M KCI had resistances of 83 M~l (SD -- 27 M,Q, n 72) measured in Na~-saline. Microelectrode capacitance was compensated avoiding overshoots in the potential response upon a current pulse applied to the microelectrode. The volume of the bathing solution in the dish was kept minimal during the measurements in order to reduce microelectrode capacitance. In this way, microelectrodes were obtained with rise times (= time to reach 66%. of the potential response upon a current pulse) lower than 0.05 msec (range 0.05-0.02 msec). Electrode tip potentials were measured according to Blatt and Slayman [4] and ranged from 0 to - 1 5 mV. All potential values have been measured with respect to the tip potential. A piezo-stepper device (Piezo-stepper P-2000, Physik lnstrumente (PI) Gmbh Co., Waldbronn-Karlsruhe, F,R.G.) was used to ensure rapid (4 /*m/0. I msec), radial (at an angle of 6(1~ from the horizontal) impalements of cells with minimal lateral vibration as opposed to impalement by hand. This device gives a minimal variation in the impalement-induced shunt resistances. The membrane-potential recordings were stored on FM magnetic tape (high frequency cut-off 20 kHz), and analyzed thereafter using a storage oscilloscope and a micro PDP-I 1 computer. Measurements were carried out at room temperature. Significance (95% level) of differences in results were tested with Student's t test. MATERIALS The hmm-cells were a kind gift of Dr. J.A, Spudich, Department of Cell Biology, Stanford University School of Medicine. Chemicals were obtained from Sigma Chemical Co.

Results PEAK POTENTIAL TRANSIENTS UPON MICROELECTRODE IMPALEMENT In our first experiments, we investigated the possibility to use intracellular microelectrodes to mea-

sure electric properties of normal D. discoideum cells such as membrane potential, resistance and capacitance. Dictyostelium cells are relatively small (diameter < 10/~m). Therefore, a peak-shaped potential transient is to be expected within the first milliseconds upon microelectrode penetration [13]. We used microelectrodes with sufficiently small rise times (<0.05 msec) to establish conditions under which fast transients could be measured. Upon touching the cell with the microelectrode a small (<4 mV) positive prepotential was seen. Figure 1A shows a typical negative-going peakshaped potential transient observed upon impalement of a D. discoideum cell with a microetectrode. The potential transient reaches a peak value Ep within 0.1 msec, which is followed by a depolarization of the membrane to a level E~. In Na+-saline, the mean values of E~ and E~ are -19.1 mV and - 4 . 7 mV (see Table), respectively. The mean time of the potential to reach two-thirds of the depolarization to En after Ep was reached, t,,, was 0.09 msec (Table) in D. discoideum cells. The EI, value measured with 4 M potassium acetate (KAc) filled microelectrodes did not differ from those measured with 3 M KC1 filled electrodes (4 M KAc: Ep = -21.0 mV (SD = 7.8 mV, n = 13)). The fact that this transient is observed already indicates that the measuring probe itself (the microelectrode) loads the potential measurement, as explained in Fig. IB, with the use of an electrical circuit representation of the measurement condition. From the two exponential potential responses (Fig. 1C) upon +150 pA current pulses applied to the microelectrode just after En was reached, we calculated the membrane resistance and capacitance. Because of the large difference between the microelectrode time constant and the time constant

126

B. Van Duijn et al.: Membrane Potential of Dictyostelmm

5 Me (mv)

A time (ms) I

I

0~

I

08

-5 En

-10 -15 -20 -25 -30

C 0.5 I

-5

time(ms) 1.0 1.5 I I

!,

-10 ~Re

-15

Ve (my} /~ -E6

Fig. 1. (A) Peak-shaped potential transient recorded upon microelectrode penetration of a D. discoideum cell bathed in Na+-saline solution. The initial positive deviation from the base line is the small prepotential seen upon touching the cell with the microelectrode. Rise time of the microelectrode was 0.03 msec. The microelectrode resistance was 84 M~. (B) Equivalent electrical circuit representation of a microelectrode measurement used in the analysis of peakshaped potential transients. Microelectrode parameters are the microelectrode resistance R~, and the microelectrode capacitance C,.. Cell parameters are the resting membrane potential Era, the membrane resistance R~,, and the membrane capacitance C,,. Impalement of the cell by the microelectrode introduces a transmembrane shunt resistance R,, associated with a diffusion potential Ej (cartoon design by C. Ince). (C) Two-component potential response to a current pulse of + 150 pA applied to the microelectrode impaled into a D. discoideum cell and recorded just after E, was reached. The component of the potential response due the microelectrode resistance and of that due to the impaled cell membrane are indicated by R~ and R,., respectively. The cell was bathed in Na--saline solution. The microelectrode rise time was 0.025 msec, and the microelectrode resistance 71 M[I. This cell showed a much more negative E,, as compared with most of the other D. discoideum cells

-20 of the i m p a l e d cell m e m b r a n e , t h e s e two time cons t a n t s c o u l d be clearly d i s t i n g u i s h e d . T h e time c o n , s t a n t of the rapid p h a s e was r e c o g n i z e d as the mic r o e l e c t r o d e time c o n s t a n t . T h e time c o n s t a n t o f the slow p h a s e was that of the p e n e t r a t e d cell m e m b r a n e . T h e m e a n m e m b r a n e c a p a c i t a n c e of D. disc o i d e u m cells w a s c a l c u l a t e d to be 6.1 p F (Table). W h e n d i v i d e d b y the e s t i m a t e d m e m b r a n e area of t h e s e s e l e c t e d D. discoideurn cells ( 2 2 0 / x m 2, SD 5 9 / z m 2, n = 10), we find for the specific c a p a c i t a n c e of the m e m b r a n e of t h e s e cells 2 . 7 / x F / c m 2 (SD = 0.4 =

/ x F / c m 2, n = 10). F u r t h e r m o r e , the i n p u t r e s i s t a n c e (Ri) of the i m p a l e d cells w a s c a l c u l a t e d from the same p o t e n t i a l r e s p o n s e s a n d was 56 Mf~ (Table) in D. discoideurn. T h e d i f f e r e n c e b e t w e e n Ep a n d En i n d i c a t e s that the m e m b r a n e r e s i s t a n c e , R , , , is m u c h larger t h a n the m i c r o e l e c t r o d e - i n d u c e d s h u n t r e s i s t a n c e , R, [13]. T h e r e f o r e , the v a l u e of Ri will be m a i n l y determ i n e d b y Rs. W e c o n c l u d e f r o m t h e s e o b s e r v a t i o n s that the stable m e m b r a n e p o t e n t i a l E~, differs f r o m the true m e m b r a n e p o t e n t i a l Era, a n d that Ep is a

B. Van Duijn et al.: M e m b r a n e Potential of Dictyostetium

better estimate of E,,, than E~. However, En may still differ from the true resting membrane potential

[13].

127

1.00Epiem 0.75-

THEORETICAL ANALYSIS

Peak transient measurements in combination with whole-cell membrane potential measurements in other types of cells showed that the peak transient can be a good estimate of the true membrane potential [13]. Whether the measured values of Ep in D. discoideum also are a fair approximation of the membrane potential may be expected to depend on the electrophysiological properties of these cells. Mathematical analysis of a microelectrode penetration measurement with the use of an electrical circuit (Fig. 1B) has shown that the membrane resistance (Rm) has little effect on the value of Ep for R,, > R, [13] (see also Appendix). The membrane capacitance (C,,,) and the microelectrode-induced shunt resistance (R,), however, strongly affect the measured value of Ep [13]. This indicates an important role for the membrane area in the accuracy of the peak transient measurements. To demonstrate the usefulness of cells with increased membrane area in the analysis of peak transient measurements, we used the equivalent electrical circuit (cf. Fig. IB) described by Ince et al. [13]. When a microelectrode enters a cell, the impaled tip is no longer exposed to the bathing solution, so the microelectrode capacity with respect to ground may slightly decrease upon impalement. We neglected this change since the dividing of the microelectrode capacitance, Ce, in a major component outside the cell and minor component (up to 25% of total C~) inside the cell upon impalement did not alter the number of exponents required to describe the circuit. In addition, the effect of this procedure on the value of Ep was negligible (<0.17%, data not shown). We calculated the value of the Ep to Em ratio (Ep/Em) as a function of Cm. R~ and C, values were taken from microelectrode measurements in normal D. discoideum cells. For Rs, the input resistance of the impaled cell measured during E~, just after the peak transient was chosen. This is valid when Rm >> Rs. The difference between Ep and En indicates that this is true for the cells used. The diffusion potential, Ed, across the microelectrode-induced shunt resistance was supposed to be zero. Figure 2 shows the exponential relationship between Ep/Em and Cm for a constant Rm. Increasing the membrane capacitance increases the value of Ep/Em. We did calculations with a nonvarying cell membrane time constant (R,~C,~), obtained by decreasing Rm with increasing Cm. Variation of R~

O50-

025-

0

12.5

25.0

]7.5

5 u.O

Cm(PF) Fig. 2. Ep to E,, ratio as a function of Cmas calculated with the use of the equivalent electrical circuit (Fig. IB). The values of the circuit parameters used here are: R,,, = 2 Gtl, R,, = 83 Mfl (27), R, = 56 M f l (14), C~ = 0.8 pF (0.6), E,,, = - 100 m V , and E,~ = 0 mV (so b e t w e e n parentheses). U p p e r curve s h o w s the relationship for the m o s t favorable conditions for Ep as a good indicator of E~. Middle curve for the m e a n conditions and the lower curve for the worst conditions

between 2 Gfl and 40 Mt~ only gave a maximal deviation in Ep's of -2.7% from the values calculated with a constant Rm of 2 Gt) (data not shown). Calculations with Ej = - 5 mV, which is the most negative value Ed can be since the mean/in is - 5 mV in these cells, did not show different Ep values within 4-3.2% as compared with the conditions used for analysis (data not shown). Figure 2 shows that the value of Ef, will approach Em closely when Cm is large enough. And because Rm only weakly influences the value of Ep, this also applies to cell size. Hence, increasing the cell size is a method to improve the reliability of Ep as an indicator of Era. Alternatively, Ep may be considered as a good indicator of Em if a further increase in cell size does not increase the value of Ep anymore. PEAK POTENTIAL TRANSIENTS IN E N L A R G E D

CELLS

In other studies, X-irradiation-derived giant murine macrophage and fibroblast cell lines did not show different values of Ep as compared with normal cells, indicating Ep to be a good estimate of the true membrane potential in these cells [12]. To find out the relation between cell size and Ep in D. discoideum, we used two types of enlarged Dictyostelium cells. First, electrofusion [23] was used to obtain large cells. The mean membrane area of the fused cells selected in our experiments was 790/zm 2 (Ta-

B. Van Duijn et al.: M e m b r a n e Potential of Dictyoszelium

128

1084le (mY)

B

lime (ms) 1

0

2

I

3

I

o

I

-10 -20

i

-30

-30

-/,,0

-z,O

-50"

-50

-6(}

-60

Ep,En!

-70

A

-80

I

4000 D

area (Urn2) 6000 I

0

-10 -20

2O00

+

+

-100-

1.5

[

f n (ms) Fig. 3.

(A) Peak potential transients m e a s u r e d in an electrofused D.

discoideum cell (b), and a hmm-cell (c) bathed in Na--saline solu-

1.0

0.5

.0

I

2000

I

'!

tion. For comparison the peak potential transient from Fig. 1A from a normal D. discoideum cell (a) is also shown. Both the increase in Ep and t, with increasing cell size are apparent. (B) Peak potential transient properties as a function of the estimated cell m e m b r a n e area of normal, electrofused and h m m D. discoideum cells. Ep (filled symbols) and E~ (open symbols) as a function of the estimated cell m e m b r a n e area of normal (circles), electrofused (circles) and hmmcells (circles). For the standard deviations of the estimated membrane areas see the Table. The squares show Ep (filled symbols) and E,, (open symbols) for hmm-cells of different size only. The estimated cell m e m b r a n e areas of these cells are: 752/xm 2 (SD = 147 b~m2, n = 66), 2144/xm 2 (SD = 266/xm 2, n = 49), and 5360/xm 2 (SD = 1361 /xm2, n = 12). Bars indicate + SD; no bar m e a n s SD < 2 inV. (C) Mean time of the potential decay to reach two-thirds of the depolarization to En after Ep was reached, t,,, as a function of the estimated cell m e m b r a n e area. The same cells and symbols as in (B). Bars indicate -+ SD

/,000 ~000 area (IJm

ble). This is about 10 times larger than that of normal cells. Figure 3A compares the negative-going peak-shaped potential transient of the three cell types used. One of these (curve b) is a potential transient observed upon impalement of an electrofused D. discoideum cell. Both Ep (-30.2 mV) and

En (-6.0 mV) are more negative in electrofused cells bathed in Na+-saline solution as compared with normal ceils (Table). The mean value of tn in these ceils was 0.13 msec (Table). The value of Ri, as measured directly after the membrane potential reached the value of

B. Van Duijn et al.: Membrane Potential of Dictyostelium

E,7, was 33 M~) (Table) in electrofused cells. The slight difference in Ri between fused and normal cells indicates that R, dominates over R .... Second, D. discoideum transformant hmm with giant cells was used. The mean membrane area of these cells selected for experiments was 1724 #m 2 (Table), about 20 times larger than in normal cells. In Figure 3A (curve c) a negative-going peakshaped potential transient observed upon impalement of a hmm-cell is shown. Membrane potentials measured in hmm-cells in Na*-saline were: E, = -38.9 mV and E,, = -12.0 mV (Table). The values of t~, Cm and Ri were determined. The value for t,~ was found to be 0.54 msec (Table). The values of C,, and Ri were 12.2 pF (Table), and 35 MFt, respectively (Table). The specific capacitance of the membrane of hmm-cells was estimated to be 1.3 b~F/cm2 (SD = 0.7 /xF/cm 2, n = 29) by dividing C,~ by the membrane area of the cells used in these experiments (mean 1169/xm 2 (so = 572/xm 2, n = 29)). The measurements in hmm-cells show an increased value of Ep, E~ and t,, as compared with normal and electrofused cells, showing a relation between cell size and Ep, as expected. Figure 3B shows measured Ep values as a function of the cell membrane area of the different cells used, suggesting a behavior of the measured Ep values as described by the equivalent electrical circuit calculations (Fig. 2). To indicate that these differences in mean Ep measured in the three cell types are only due to variations in membrane capacitance and not due to the different origins of these cells, Fig. 3B also shows Ep as a function of membrane area of hmm-cells. The dependence of Ev on the membrane area of the hmm-cells indicates that variation in membrane area for one cell type also leads to variation in the Ep measured, assuming that the true membrane potential does not depend on the cell size. This is evidence that the measured peak transient values in normal D. discoideum cells are not near to the true membrane potential. However, the E~ values measured in enlarged cells are closer to true membrane potential of D. discoideum. Figure 3C shows the relationship between tn and the cell membrane area for the same cells as in Fig. 3B. From the model, it is expected that t~ will be mainly determined by RsC~ [13]. RiC~ is proportional to the membrane area for cells with R,~ > R,. Therefore, the linear relationship between tn and the membrane area shown in Fig. 3C is as expected for D. discoideum cells.

129

between membrane resistance, microelectrode-induced shunt resistance, membrane potential and diffusion potential of the shunt [13],

E, = (E,,R, + EdR,,~)/(R,n + R0.

(1)

From Eq. (1), it follows that the smaller R,,, (i.e., the larger the cells) the more E~ approaches the value of Era. Figure 3B shows the values of En for the different cell types as a function of the membrane area. As expected from Eq. (1), the value of E~ is more negative for larger cells, consistent with the lower membrane resistance they have. Figure 3B also shows that Ep is always closer to the true membrane potential than E,. Furthermore, this figure reveals that a much stronger enlargement of cells is required for E~ than for Ep to approach Era.

ESTIMATION OF THE TRUE RESTING MEMBRANE POTENTIAL

Although the microelectrode measurements in Dictyostelium suffer from a loading shunt resistance, an estimation of the true resting membrane potential can still be made. Simulation of the rapid potential transients upon microelectrode impalement (Fig. 2) using parameter values as found in our experiments indicates a value for Ep/Em of 0.39 for impalements of normal D. discoideum cells. This suggests that Em is much more negative than the measured value of Ep. The measurements in the larger cells (Fig. 3A and B) support this evidence. We made an estimation of E~ from the Ep/Em values (Fig. 2) for normal, fused and hmm-cells using the membrane capacitance of the different cell types (Table). In this way we find for normal D. discoideurn cells, Em = -50 mV (range -30 to -110 mV), for electrofused cells, E m = -46 mV (range -33 to - 6 6 mV) and for hmm-cells, E~ = -50 mV (range -40 to -65 mV). This method for making an approximation of the true membrane potential is rather unsatisfactory, since the range of these estimations is large, especially for the normal cells. Another way to obtain an approximate value of Em is extrapolation of the Ep data in Fig. 3B. Single exponential fitting of the Ep data points (according to Fig. 2) indicates that the membrane potential of Dictyostelium cells (i.e., the Ep value for extreme large membrane area) is -67 -+ 13 mV (fitting with Gauss-Newton method, correlation coefficient =

0.98). THE SHUNTED MEMBRANE POTENTIAL

In contrast with Ep, the value of E~ does not depend on C~ but on Rm. E~ follows from the relationship

Occasionally in hmm-cells, Ep values around -80 mV were measured (mean of 10 largest Ep values measured = - 8 2 mV, SD = 8 mV). This suggests that the membrane potential of these cells can

130

B. Van Duijn et al.: Membrane Potential of

10 . . . . . .

I

Ke(rnH) 100 . . . . .

I

-10

iI

-20

-3O Ep, En(mV)

i

-~0 Fig, 4. E~ (filled symbols) and E,, (open symbols) as a function of the extracellular p o t a s s i u m concentration, K , , in the bath. Ep and En were m e a s u r e d in hmm-cells with an estimated cell membrane area of 1275/xm 2 (SD -- 308 /xm 2, n = 96). Bars indicate + SD; n = 32 for each concentration

be at least - 8 0 mV in Na+-saline solution, which is in agreement with the data from Fig. 3B. DIFFERENT

IONIC CONDITIONS

Dictyostelium

because En is a bad indicator of the true membrane potential. Ep measured in cells bathed for more than 30 min in K+-saline solution were more negative than just after exchanging the Na+-saline solution for the K+-saline solution. This indicates that the membrane potential recovers from the initial depolarization. The action of electrogenic ion pumps and/or active ion transport might play a role in this recovery. Patch-clamp measurements in the cell-attached patch mode have been done by others on D. discoideum cells bathed in calcium-saline solutions [22]. In order to provide membrane potential estimates for this type of experiments, we did membrane potential measurements on hmm-cells bathed in Ca2+-saline solution. Membrane potentials under these conditions were: Ep = - 3 2 . 7 mV (SD = 12.6 mV, n = 10), and E~ = - 1 2 . 8 mV (SD = 10.9 mV, n = 10). Control measurements in Na+-saline solution (with 1 mM CaCI2) resulted in Ep = - 3 1 . 8 mV (SD = 13.0 mV, n = 19), and E~ = - 1 3 . 0 mV (SD = 4.3 mV, n = 19). Thus, there is no difference in membrane potential between cells bathed in CaZ+-saline solution and in Na+-saline solution (significant at 95% level).

MICROELECTRODE-IN DUCED HYPERPOLARIZ1NG RESPONSE

Though the electrophysiological conditions of the

D. discoideum cells change upon impalement, it is The dependence of the membrane potential of Dictyostelium on different ionic conditions was investigated in order to explore the ionic mechanism of the membrane potential. Changing the Na+-saline solution for the K +saline solution or for a mixture of these solutions resulted in changed membrane potentials. These changes were measured within 15 min after the solution change. Figure 4 shows Ep and En for different extracellular K + concentrations for hmm-cells. Hmm-cells were used because potential changes could be measured more reliably in these cells (see above). H o w e v e r , normal D. discoideum cells also showed a less negative Ep in K+-saline solution: Ep = - 1 4 . 7 mV (SD = 4.5 mV, n = 19). In control measurements in Na+-saline solution we found: E~ = - 1 9 . 2 mV (SD = 4.3 mV, n = 15) (significant at 95% level). Figure 4 shows that Ep is dependent on the extracellular K + concentration, which implies that the membrane potential of D. discoideum is dependent on extracellular potassium. As expected, En only shows a weak dependency on the extracellular potassium concentration,

still of interest to study the membrane properties of the impaled cell. Certain ionic conductances may be expressed due to the damage [12, 28], or may still be measurable in spite of the microelectrode-induced shunt resistance. After reaching En, the membrane potential in many cases (>60%) hyperpolarizes to a maximal negative potential Eh (Fig. 5). This hyperpolarization is accompanied by an increase in transmembrane resistance, which likely reflects an increase in the microelectrode-induced shunt resistance by a sealing of the membrane around the microelectrode [4]. When the Eh value is reached, the membrane slowly depolarizes again, with a half time of depolarization, Tv2, to a sustained steady-state potential. The depolarization is accompanied by a decrease in transmembrane resistance (Fig. 5). The Eh and TI/z values for normal D. discoideum, fused cells and hmm-cells bathed in Na +saline solution are given in the table. From these measurements it is clear that the Eh values are less negative than the Ep values measured in the same cells (Table). In addition, Eh is not strongly dependent on the cell size, in contrast with the value of Ep

13. Van Duijn et al.: Membrane Potential of Dictyostelium

10mVI ; FP--- i

Eh---

lrilIl'"' .....

' s s'

Fig. 5. Slow membrane potential changes upon microelectrode impalement into a D. discoideum cell bathed in Ca-'+-salinesolution. Upon touching of the cell a small positive prepotential is seen. The initial rapid impalement peak potential transient, indicated by Ep, cannot be seen in this record because of the low high-frequency cut-off properties of the chart recorder used. Current pulses of 26 pA were applied to the microelectrode to monitor the input resistance, Ri. Microetectrode resistance was 107 Mfl

(Fig. 3B), H o w e v e r , the half time of depolarization, Tv2, increases with increasing cell size. In 4 hmm-cells (out of 49), a stable potential of - 2 1 . 8 m V (range - 1 4 . 4 to - 2 9 . 6 mV) could be maintained for a b o u t three rain. The corresponding Ep values of these four cells were much more negative than the stable potential values (Ep = - 5 4 . 2 mV, range - 2 4 . 8 to - 9 1 . 9 mV). Dictyostelium cells bathed in Ca2+-saline solution showed a more negative hyperpolarization, Eh = - 1 9 . 0 m V (so = 2.0 mV, n = 45), as c o m p a r e d with cells bathed in Na+-saline solution (significant at 95% level). H o w e v e r , T~/? was not increased in CaZ+-saline solution (TI/2 = 1.4 sec, s o = 0.2 sec, n = 45) (significant at 95% level). In all e x p e r i m e n t s there was no correlation between the value of Eh and the value of Tv2. The increase of Tm with increasing cell size indicates a possible role in the depolarization for the leakage of ions f r o m the microelectrode into the cell. In order to find out whether this depolarization in Dictyostelium cells is caused by the leakage of chloride ions from the microelectrode into the cell as is the case in Neurospora cells [4] we did some additional e x p e r i m e n t s with different microelectrode fillings, in which C1- was lacking or strongly reduced. We did m e a s u r e m e n t s with 4 M KAc-filled microelectrodes on normal Dictyostelium cells bathed in CaZ+-saline solution and on hmm-cells bathed in Na+-saline solution. The value of Eh in the normal cells was - 1 7 . 0 m V (SD = 2.0 mV, n = 14), and of Tv2 was 1.7 sec (SD = 0.5 sec, n = 14). N o hyperpolarized potentials stable at Eh were observed in these cells with the use of 4 M KAc-filled microelectrodes. In the hmm-cells, Eh was --12.6 mV (SD = 6.7 mV, n = 11), which is not different from Eh m e a s u r e d with 3 M KCl-filled microelectrodes (significant at 95% level). Tm ranged f r o m 4 sec to 3 rain

131 (mean 64 sec) when 4 M KAc-filled microelectrodes were used on hmm-cells. Nevertheless, stable potentials around or more negative than Ep were neither obtained on hmm-cells with the use of 4 M KAc-filled microelectrodes. M e a s u r e m e n t s with 0.1 M KCl-filled microelectrodes on normal D. discoideum cells bathed in Ca2+-saline solution neither showed stable potentials around the Ep nor at the Eh value. Instead, a large variation in both Eh and T~/2 was found. The m e a n Eh was --34.2 mV (SD = 30.1 mV, n = 10) and the mean T~/2 was 30 sec (range 5 sec to 3 min, n = I0).

Discussion The present study shows that microelectrode measurements in D. discoideum cells, when applied properly, can provide information about the electrical m e m b r a n e properties of these cells. This has also been shown for various other high-resistance cell types [2, 13, 16, 18, 24]. The a p p e a r a n c e of a rapid p e a k - s h a p e d potential transient (Figs. 1A and 3A) upon microelectrode impalement of a D. discoideum cell shows the presence of a microelectrode-induced shunt resistance, which causes a sustained depolarization of the m e m b r a n e potential. H o w e v e r , our results show that the peak transient value Ep of the rapid impalement transient is still the best available estimate for the true resting m e m brane potential of D. discoideum. F r o m the shape of the potential decay after Ep is reached (Figs. 1A and 3A) we conclude that changes in the microelectrode-induced shunt resistance during the potential transient are not significant in disturbing our measurements. The sealing of the m e m b r a n e around the microelectrode, associated with an increase in shunt resistance, appears to occur on a larger time scale (see microelectrodeinduced hyperpolarizing response and [4]). M e a s u r e m e n t s in enlarged cells proved to be a good method to test the reliability of Ep as a measure of Era. F r o m the dependence of the measured peak transient potential on the cell size between the different cell types used (normal, fused and hmm) as well as within one cell type (Fig. 3A and B) we conclude that the true m e m b r a n e potential of these different cell types is the same (assumed that Em is cell size independent). An estimation of the true m e m b r a n e potential was made f r o m the simulations, from the d e p e n d e n c e of Ep on the cell size and the occasionally appearing larger Ep values in hmm-cells. F r o m these data, Em was approximated to be at least - 5 0 mV in Na+-saline solution for all the cell types used. The m e a s u r e m e n t s in hmm-cells indicate that Em likely lies around - 8 0 m V for D. discoideum cells in Na+-saline solution. Measure-

132

B. Van Duijn et al.: Membrane Potential of

ments of the intracellular sodium (minimal about 5 mM) and potassium concentrations (maximal about 50 mM) of D. discoideum have been done by others [1, 19, 21]. The Nernst potential for K + and Na + in cells bathed in Na+-saline solution are -60 mV and +55 mV, respectively. The change of the peak transient upon changing of the external potassium concentration (Fig. 4) indicates that the membrane potential is dependent on selective potassium conduction. This dependency on the external K + concentration suggests the presence of a K + conductance, which could be due to K § channel activity in these cells [22]. A membrane potential of -90 mV in the true slime mold Physarum polycephalum was found by Hato and coworkers [10] with microelectrodes. In Amoeba proteus a membrane potential of -72 mV was reported, which is dependent on the extracellular K + concentration [3]. The estimation of the true membrane potential of D. discoideum and peak transients, which have been measured in hmm-cells, show that the true membrane potential is more negative than the Nernst potential for potassium for both Na +- and K*-saline solution. From this we conclude that electrogenic ion pumps also contribute to the membrane potential of D. discoideum. Experiments using ion pump blocking agents and different ion solutions are required to determine the contribution and nature of such factors to the membrane potential. The shunted membrane potential, E~, is less negative than Ep. Hence, R,~ is large if compared with the microelectrode-induced shunt resistance. For larger cells, the value of E,, is more negative than for normal cells, which shows that the membrane resistance, Rm, becomes smaller with increasing cell size. Since E, follows from the relationship between Rm, Rs, Em and Ej, Eq. (1), an estimation of Rm can be made. For Ed = 0, Eq. (1) reduces to:

E,/E,~ = R,/(Rm + R,) = Ri/Rm.

(2)

Therefore, with the estimated value of Era, and the measured values of E~ and Ri, a minimum value for Rm can be calculated using Eq. (2). For normal D. discoideum cells, we find in this way for R,,, at least 1 Gf~. For fused and hmm-cells we find 440 and 230 MEt, respectively. Since Ri is much smaller than Rm, the measured input resistance of the impaled cells will be dominated by R;. The calculation of the specific membrane capacitance of Dictyosteliurn revealed a value between 1 and 3 /xF/cm2 for normal and hmm-cells. This outcome, together with the linear relationship found between tn and the estimated cell membrane area, shows that the estimations of the membrane

Dictyostelium

areas of these cells are of the right order of magnitude, as a value around 1 /xF/cm 2 is commonly found for the specific capacitance of biological membranes [I 1]. A more negative membrane potential is expected in cells bathed in Ca2+-saline solution, since this solution does not contain potassium, as compared with cells bathed in Na+-saline solution. Our measurements show that no difference in membrane potential is present between cells bathed in Na+-saline and CaZ+-saline solution. This might be due to blockage of potassium-dependent electrogenic ion pumps by low extracellular potassium concentrations [9], which depolarizes the membrane. The slow hyperpolarization followed by a depolarization occurring after the microelectrode-induced peak potential transient shows that, even in high-resistance cells, microelectrodes can be used to measure certain changes in electrophysiological properties while the cells are impaled. In various cells, transient hyperpolarizations upon microelectrode penetration have been reported [4, 10, 12, 15, 25, 28]. These measurements, however, show microelectrode-induced hyperpolarizations accompanied by a decrease in transmembrane resistance, except for Neurospora cells [4]. In Neurospora cells, the hyperpolarization is accompanied by an increase in transmembrane resistance and is caused by a sealing of the cell membrane around the microelectrode. This sealing makes R~ larger so that the measured potential will be closer to E,~ (see Eq. (1)). In addition, electrogenic ion pump currents will generate a larger potential when the input resistance of the cell increases. The Ep values measured in Na+-saline solution and Ca2+-saline solution are not different. Therefore, the larger EI~ values found in cells bathed in Ca2+-saline solution as compared with cells bathed in Na*-saline solution might be due to a better sealing of the membrane around the microelectrode for higher calcium concentrations. Because no correlation is present between Eh and Tv2, the magnitude of the microetectrode-induced shunt resistance Rs, which determines the value of Ek reached, has no influence on the rate of depolarization. Hence, leakage through R~ of ions from the bath solution into the cell likely does not play an essential role in the depolarization of the measured potential after Eh is reached. The increase of the half time of depolarization, T1/2, with increasing cell size and the increase of T1/2 when 0.1 M KCl-filled microelectrodes are used suggests that the depolarization is caused by leakage of ions from the microelectrode into the cell as is the

B. Van Duijn et al.: Membrane Potential of Dictvo.stelium

case with leakage of chloride ions from the microelectrode in Neurospora cells [4]. On the other hand, the experiments with 4 M KAc-filled microelectrodes do not confirm a role for leakage of chloride ions into the cell. Although the value of Eh and T~/2 could be changed with the use of different microelectrode fillings, we have not been able to record stable potentials with values around or more negative than the measured values of Ep. Therefore, the peak value Ep of the initial rapid impalement transient remains to be the best estimate of the membrane potential of D. discoideum cells. We conclude that leakage of ions from the microelectrode plays a role in the slow depolarization of the membrane potential after Eh. However, other processes (e.g., changes in the sealing of the membrane around the microelectrode), which prevent the recording of stable potentials, will be present as well and need further investigation. The present study shows that useful information about electrophysiological properties can be obtained by careful application of the microelectrode technique, even in small, high-resistance cells like D. discoideum. Our results concern the membrane potential, resistance and capacitance of nonstimulated D. discoideum cells. We consider these results as a basis for future research into the role of transmembrane currents and potentials in the response of D. discoideum to chemoattractants. The authors wish to thank Dr. Ir. Can Ince, Dr. Peter J.M. Van Haastert, Henk P. Buisman, Johan E. Pinas, Prof. Dr. A.A. Verveen and Prof. Dr. T.M. Konijn for advice, support and stimulating discussions. We are very grateful to Kees Donkersloot for the design and the construction of the cell fusion instrument and Jan Van Hartevelt for computer assistance. We acknowledge the Foundation for Medical Research (MEDIGON) of the Netherlands and the Department of Infectious Diseases (Prof. Dr. R. van Furth) for the use of computer equipment for data processing.

References

133 6. Bumann, J., Wurster, B., Malchow, D. 1984. Attractantinduced changes and oscillations of the extracellular Ca > concentration in suspensions of differentiating Dictyostelium cells. J. Cell Biol. 98:173-178 7. De Lozanne, A., Spudich, J.A. 1987. Disruption of the Dictyostelium myosin heavy chain gene by homologous recombination. Science 236:1086-1091 8. Devreotes, P.N. 1983. Cyclic nucleotides and cell-cell communication in Dictyostelium discoideum. Adv. Cycl. Nucleotide Res. 15:55-96 9. Gorman, A.L.F., Marmor, M.F. 1970. Temperature dependence of the sodium-potassium permeability ratio of molluscan neuron. J. Physiol. (London) 210:919-931 10. Hato, M., Ueda, T., Kurihara, K., Kobatake, Y. 1976. Changes in zeta potential and membrane potential of the slime mold Physarum polycephalum in response to chemical stimuli. Biochim. Biophys. Acta 426:73-80 11. Hille, B. 1984. Ionic Channels of Excitable Membranes. Sinauer Associates, Sunderland, Massachusetts 12. [nce, C., Leijh, P.C.J., Meijer, J.. Van Bavel, E., Ypey, D.L. 1984. Oscillatory hyperpolarizations and resting membrane potentials of mouse fibroblast and macrophage cell lines. J. Physiol. (London)352:625-635 13. Ince, C., Van Bavel, E., Van Duijn, B., Donkersloot, K., Coremans, A., Ypey, D.L., Verveen, A.A. 1986. Intracellular microelectrode measurements in small ceils evaluated with the patch clamp technique. Biophys. J. 50:1203-1209 14. Ince, C., Van Dissel, J.T., Diesselhoff, M.M.C. 1985. A Teflon culture dish for high-magnification microscopy and measurements in single cells. Pflueg, ers Arch. 403:240-244 15. Ince, C., Van Duijn, B., Ypey, D.L., Van Bavel, E., Weidema, F., Leijh, P.C.J. 1987. Ionic channels and membrane hyperpolarization in human macrophages. J. Membrane Biol. 97:251-258 16. Ince, C., Ypey, D.L., Van Furth, R., Verveen, A.A. 1983. Estimation of the membrane potential of cultured macrophages from the fast potential transient upon microelectrode entry. J. Cell Biol. 96:796-801 17. Konijn, T.M., Van de Meene, J.G.C., Bonner, J.T., Barkley, D.S. 1967. The acrasin activity of adenosine-Y,5'cyclic phosphate. Proc. Natl. Acad. Sci. USA 58:1152-1154 18. Lassen, U.V., Nielsen, A.M.T., Pape, L., Simonsen, L.O. 1971. The membrane potential of Ehrlich ascites tumor cells: Microelectrode measurements and their critical evaluation. J. Membrane Biol. 6:269-288 19. Maeda, M. 1983. Alteration of cellular ionic constituents by external ionic conditions, and its significance in the development of Dictyostelium discoideum. Bot. Mug. (Tokyo) 96:193-210

I. Aeckerle, S., Wurster, B., Malchow, D. 1985. Oscillations and cyclic AMP-induced changes of the K + concentration in Dictyostelium discoideum. EMBO J. 4:39-43 2. Bakker, R., Dobbelmann, J., Borst-Pauwels, G.W.F.H. 1986. Membrane potential in the yeast Endomyces magnusii measured by microelectrodes and TPP + distribution. Biochim. Biophys. Acta 861:205-209 3. Bingley, M.S., Thompson, C.M. 1962. Bioelectric potentials in relation to movement in Amoebae. J. Theor. Biol. 2:16-32 4. Blatt, M.R., Slayman, C. L. 1983. KCI leakage from microelectrodes and its impact on the membrane parameters of a nonexcitable cell. J. Membrane Biol. 72:223-234 5. Bumann, J., Malchow, D., Wurster, B. 1986. Oscillations of Ca 2+ concentration during the cell differentiation of Dictyostelium discoideum. Differentiation 31:85-91

20. Malchow, D., Bohme, R., Gras, U. 1982. On the role of calcium in chemotaxis and oscillations of Dictyostelium cells. Biophys. Struct. Mech. 9:131-136 21. Marin, F.T., Rothman, F.G. 1980. Regulation of development in DictyosteIium discoideum IV. Effects of ions on the rate of differentiation and cellular response to cyclic AMP. J. Cell Biol. 87:823-827 22. Muller, U., Malchow, D., Hartung, K. 1986. Single ion channels in the slime mold Dictyostelium discoideum. Bioehim. Biophys. Acta 857:287-290 23. Neumann, E., Gerisch, G., Opatz, K. 1980. Cell fusion induced by electric impulses applied to Dictyostelium. Naturwissenschaften 67:414-415 24. Peres, A., Bernardini, G., Negrini, C. 1986. Membrane potential measurements of unfertilized and fertilized Xenopus

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laevis eggs are affected by damage caused by the electrode. Exp. Cell Res. 162:159-168 25. Persechini, P.M., Araujo, E.G., Oliveira-Castro, G.M. 1981. Electrophysiology of phagocytic membranes: Induction of slow membrane hyperpolarizations in macrophages and macrophage polykaryons by intracellular calcium injection. J. Membrane Biol. 61:81-90 26. Peters, D.J.M., Knecht, D.A., Loomis, W.F., DeLozanne, A., Spudich, J., Van Haastert, P.J.M. 1988. Signal transduction, chemotaxis and cell aggregation in Dictyostelium discoideum cells without myosin heavy chain. Dev. Biol.

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27. Van Haastert, P.J.M., Konijn, T.M. 1982. Signal transduction in the cellular slime molds. Mol. Cell. Endoerinol. 26:117 28. Walsh, J.V., Jr., Singer, J.J. 1980. Penetration-induced hyperpolarization as evidence for Ca > activation of K~ conductance in isolated smooth muscle cells. Am. J, Physiol. 239:C 182-C 189

Received 25 March 1988; revised 1 August 1988

Appendix For convenience of the reader a summary is given of the mathematical analysis, carried out by Ince et al. [13], of a microelectrode measurement as represented by the electrical equivalent circuit of Fig. lB. We assume that the circuit components are constant during the impalement transient. At the moment of impalement (t = 0), a connection between Re, Rs, Rm and C,~ is made (as shown in Fig. IB). Subsequently C,~ will discharge from E,,, to a new steady-state potential level E,,. If the response time of the microelectrode is sufficiently rapid, the discharge of Cm can be monitored at V~. At t = 0, according to Kirchhoff's laws, the sum of the currents flowing through Rm, Cm, R~ and R,, must be zero. Furthermore, the current through Re equals the current through C,. (assuming ideal input characteristics of the potential meter Ve). From this, the following relation between the measured potential Ve and the membrane potential E,~ is found: d2Ve dV~ R., T~T~ ~ . + (T~ + Tc + f i T e ) - ~ + fiV,, = ~ E j + E,~ (3) in which

Tm =

RmCm,

Te = ReC,,,

1",- = RmCe

and

fi - (R~ + R.,)/R~.

In the steady-state condition (t--+ ~c), Eq. (3) reduces to Eq. (1), where V~, = E,. Only for measurements where R, > Rm (e.g., in patchclamp measurements) Eq. (1) reduces to E, = Era. When R~ is in the order of magnitude of Rm, however, measurement of the peak potential Ep provides a more accurate measure of E,~ than does E,. Since all coefficients in Eq. (3) are positive, the solution of Eq. (3) will be of the form:

V~ = A exp (Qit) + B exp (Q2t).

(4)

From the characteristic equation and the initial conditions (V~ = 0 and dVe/dt = E,,/T,, at time t = 0) the factors Q~, Q:, A and B can be calculated. The factors A, B, Q~ and Q2 are respectively: A = (Em/T~. + Q2E~)/(QI - Q2)

and

B = -(E,jT~, + Q,E,,)/(Qj - Q2)

QI ,Q2 =

(1",, + r

(5)

+ Tc) +- [(T,, + /3/',, + L): - 4BT,,L] I': 2T~T~,

(6) From the model and the mathematical description it is clear that Em cannot be calculated by exponential extrapolation back to the moment of cell penetration of the depolarizing tail of the impalement transient as proposed by Lassen et al. [18]. This is due to the presence of the capacitive load imposed by C,, on the discharge of the membrane. The value of E~ can be calculated by substitution of Q~, Q2, A and B and of t0 (i.e., the time it takes V,, to reach Ep) in Eq. (4) [13]. The value of Ep is given by: Ep = A ( - Q I A / Q z B ) Q ' " Q 2 - O ~ '

+ B(-QtA/Q2B)Q'-/(Qz-Q~)

+ E,,.

(7) A more detailed analysis of the model behavior under various conditions is described by Ince et al. [13].